A federal grand jury in Tucson has begun hearing evidence in a controversial 1976 case involving the alleged torture of three Mexican workers near the Arizona border town of Douglas.

During the past three years the case h-s heightened tensions along the border, created embarrassing political problems for the Carter administration and captured the attention of Hispanic groups around the country who claim Hispanics have been the victims of a rising tide of violence.

The grand jury investigation is seen as landmark by activists in southern Arizona because it is the first time the federal government has entered such a case on the side of allegedly victimized undocumented aliens.

Two fo the three victims who claim they were tortured, Elezar Ruelas, 27, and Manuel Garcia, 28, reportedly arrived last week in Tucson from Mexico to testify before the grand jury.

Ruelas, Garcia and a third man, Bernabe Herrera-Mata, say they crossed the border on Aug. 18, 1976, in search of jobs when they were taken at gunpoint to the ranch of George Hanigan, a prominent Douglas rancher.

The three men say Hanigan and his two sons, Patrick and Thomas, mistook them for robbers and, using hot pokers, cigarettes, knives and a shotgun filled with birdshot, tortured and beat them for several hours before sending them fleeting, naked and bleeding back across the border.

A year after the incident, local authorities charged the Hanigans with 14 counts of kidnaping, assault and robbery. George Hanigan died before the trial and in October 1977 an all-Anglo jury, after 18 hours of deliberation, cleared the Hanigan brothers on all counts. The verdict set off a storm of protest in Mexico and in Mexican-American communities along the border. Mexican Consul Raul Avelyera said it "declared open season on illegal aliens."

Activists in Douglas organized demonstrations and a week-long boycott of white-owned businesses on the U.S. side of the border. A national coalition of Mexican-American groups petitioned the Justice Department for a civil rights probe.

When then-Deputy U.S. Attorney General Benjamin Civiletti toured the Southwest in November 1978, in response to a growing conviction among Hispanics that the Carter administration had become insensitive to their civil liberties, minority leaders cited the Hanigan case as a test of the government's concern about Mexican Americans.

After Civiletti's visit, the Justice Department announced a new probe of the Hanigan incident.

The grand jury, which began hearing evidence last week, could bring charges against the Hanigan brothers on possible violations of civil rights, immigration and other federal laws.

"We're not off on a fishing expedition," said Michael Hawkins, U.S. Attorney for Arizona. "We know exactly what statutes we are looking at."

Hispanic leaders stress that the violence allegedly associated with the Hanigan case is not isolated. Hispanic groups claim there have been at least 15 killings and more than 150 incidents of alleged brutality against Mexican-Americans, mainly by law-enforcement officials, during the last three years. In Arizona alone, there were three instances of undocumented aliens being shot and wounded by federal Border Patrol agents during the past 18 months.

"The outcome of the [Hanigan] case will set precendents that will have an effect on many cases of brutality, both from the police and from private citizens, against undocumented aliens," said Raul Yzaguirre, president of the National Council of LaRaza.

"None of us who have been involved with the Hanigan case at all are particularly interested in sticking the Hanigan brothers in jail," said Margo Cowan, the director of the Manzo Area Council, a Tucson social service organization. "That's not the issue. What's at issue is that historically in the Southwest undocumented people have been the brunt of all sorts of violent activities by law enforcement officials, Border Patrolmen, employers, growers, transporters."